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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.linear;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.MaxCountExceededException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.NullArgumentException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.util.IterationManager;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.util.MathUtils;<a name="line.23"></a>
<FONT color="green">024</FONT>    <a name="line.24"></a>
<FONT color="green">025</FONT>    /**<a name="line.25"></a>
<FONT color="green">026</FONT>     * &lt;p&gt;<a name="line.26"></a>
<FONT color="green">027</FONT>     * This abstract class defines preconditioned iterative solvers. When A is<a name="line.27"></a>
<FONT color="green">028</FONT>     * ill-conditioned, instead of solving system A &amp;middot; x = b directly, it is<a name="line.28"></a>
<FONT color="green">029</FONT>     * preferable to solve either<a name="line.29"></a>
<FONT color="green">030</FONT>     * &lt;center&gt;<a name="line.30"></a>
<FONT color="green">031</FONT>     * (M &amp;middot; A) &amp;middot; x = M &amp;middot; b<a name="line.31"></a>
<FONT color="green">032</FONT>     * &lt;/center&gt;<a name="line.32"></a>
<FONT color="green">033</FONT>     * (left preconditioning), or<a name="line.33"></a>
<FONT color="green">034</FONT>     * &lt;center&gt;<a name="line.34"></a>
<FONT color="green">035</FONT>     * (A &amp;middot; M) &amp;middot; y = b, &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;followed by<a name="line.35"></a>
<FONT color="green">036</FONT>     * M &amp;middot; y = x<a name="line.36"></a>
<FONT color="green">037</FONT>     * &lt;/center&gt;<a name="line.37"></a>
<FONT color="green">038</FONT>     * (right preconditioning), where M approximates in some way A&lt;sup&gt;-1&lt;/sup&gt;,<a name="line.38"></a>
<FONT color="green">039</FONT>     * while matrix-vector products of the type M &amp;middot; y remain comparatively<a name="line.39"></a>
<FONT color="green">040</FONT>     * easy to compute. In this library, M (not M&lt;sup&gt;-1&lt;/sup&gt;!) is called the<a name="line.40"></a>
<FONT color="green">041</FONT>     * &lt;em&gt;preconditionner&lt;/em&gt;.<a name="line.41"></a>
<FONT color="green">042</FONT>     * &lt;/p&gt;<a name="line.42"></a>
<FONT color="green">043</FONT>     * &lt;p&gt;<a name="line.43"></a>
<FONT color="green">044</FONT>     * Concrete implementations of this abstract class must be provided with the<a name="line.44"></a>
<FONT color="green">045</FONT>     * preconditioner M, as a {@link RealLinearOperator}.<a name="line.45"></a>
<FONT color="green">046</FONT>     * &lt;/p&gt;<a name="line.46"></a>
<FONT color="green">047</FONT>     *<a name="line.47"></a>
<FONT color="green">048</FONT>     * @version $Id: PreconditionedIterativeLinearSolver.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.48"></a>
<FONT color="green">049</FONT>     * @since 3.0<a name="line.49"></a>
<FONT color="green">050</FONT>     */<a name="line.50"></a>
<FONT color="green">051</FONT>    public abstract class PreconditionedIterativeLinearSolver<a name="line.51"></a>
<FONT color="green">052</FONT>        extends IterativeLinearSolver {<a name="line.52"></a>
<FONT color="green">053</FONT>    <a name="line.53"></a>
<FONT color="green">054</FONT>        /**<a name="line.54"></a>
<FONT color="green">055</FONT>         * Creates a new instance of this class, with default iteration manager.<a name="line.55"></a>
<FONT color="green">056</FONT>         *<a name="line.56"></a>
<FONT color="green">057</FONT>         * @param maxIterations the maximum number of iterations<a name="line.57"></a>
<FONT color="green">058</FONT>         */<a name="line.58"></a>
<FONT color="green">059</FONT>        public PreconditionedIterativeLinearSolver(final int maxIterations) {<a name="line.59"></a>
<FONT color="green">060</FONT>            super(maxIterations);<a name="line.60"></a>
<FONT color="green">061</FONT>        }<a name="line.61"></a>
<FONT color="green">062</FONT>    <a name="line.62"></a>
<FONT color="green">063</FONT>        /**<a name="line.63"></a>
<FONT color="green">064</FONT>         * Creates a new instance of this class, with custom iteration manager.<a name="line.64"></a>
<FONT color="green">065</FONT>         *<a name="line.65"></a>
<FONT color="green">066</FONT>         * @param manager the custom iteration manager<a name="line.66"></a>
<FONT color="green">067</FONT>         * @throws NullArgumentException if {@code manager} is {@code null}<a name="line.67"></a>
<FONT color="green">068</FONT>         */<a name="line.68"></a>
<FONT color="green">069</FONT>        public PreconditionedIterativeLinearSolver(final IterationManager manager)<a name="line.69"></a>
<FONT color="green">070</FONT>            throws NullArgumentException {<a name="line.70"></a>
<FONT color="green">071</FONT>            super(manager);<a name="line.71"></a>
<FONT color="green">072</FONT>        }<a name="line.72"></a>
<FONT color="green">073</FONT>    <a name="line.73"></a>
<FONT color="green">074</FONT>        /**<a name="line.74"></a>
<FONT color="green">075</FONT>         * Returns an estimate of the solution to the linear system A &amp;middot; x =<a name="line.75"></a>
<FONT color="green">076</FONT>         * b.<a name="line.76"></a>
<FONT color="green">077</FONT>         *<a name="line.77"></a>
<FONT color="green">078</FONT>         * @param a the linear operator A of the system<a name="line.78"></a>
<FONT color="green">079</FONT>         * @param m the preconditioner, M (can be {@code null})<a name="line.79"></a>
<FONT color="green">080</FONT>         * @param b the right-hand side vector<a name="line.80"></a>
<FONT color="green">081</FONT>         * @param x0 the initial guess of the solution<a name="line.81"></a>
<FONT color="green">082</FONT>         * @return a new vector containing the solution<a name="line.82"></a>
<FONT color="green">083</FONT>         * @throws NullArgumentException if one of the parameters is {@code null}<a name="line.83"></a>
<FONT color="green">084</FONT>         * @throws NonSquareOperatorException if {@code a} or {@code m} is not<a name="line.84"></a>
<FONT color="green">085</FONT>         * square<a name="line.85"></a>
<FONT color="green">086</FONT>         * @throws DimensionMismatchException if {@code m}, {@code b} or<a name="line.86"></a>
<FONT color="green">087</FONT>         * {@code x0} have dimensions inconsistent with {@code a}<a name="line.87"></a>
<FONT color="green">088</FONT>         * @throws MaxCountExceededException at exhaustion of the iteration count,<a name="line.88"></a>
<FONT color="green">089</FONT>         * unless a custom<a name="line.89"></a>
<FONT color="green">090</FONT>         * {@link org.apache.commons.math3.util.Incrementor.MaxCountExceededCallback callback}<a name="line.90"></a>
<FONT color="green">091</FONT>         * has been set at construction of the {@link IterationManager}<a name="line.91"></a>
<FONT color="green">092</FONT>         */<a name="line.92"></a>
<FONT color="green">093</FONT>        public RealVector solve(final RealLinearOperator a,<a name="line.93"></a>
<FONT color="green">094</FONT>            final RealLinearOperator m, final RealVector b, final RealVector x0)<a name="line.94"></a>
<FONT color="green">095</FONT>            throws NullArgumentException, NonSquareOperatorException,<a name="line.95"></a>
<FONT color="green">096</FONT>            DimensionMismatchException, MaxCountExceededException {<a name="line.96"></a>
<FONT color="green">097</FONT>            MathUtils.checkNotNull(x0);<a name="line.97"></a>
<FONT color="green">098</FONT>            return solveInPlace(a, m, b, x0.copy());<a name="line.98"></a>
<FONT color="green">099</FONT>        }<a name="line.99"></a>
<FONT color="green">100</FONT>    <a name="line.100"></a>
<FONT color="green">101</FONT>        /** {@inheritDoc} */<a name="line.101"></a>
<FONT color="green">102</FONT>        @Override<a name="line.102"></a>
<FONT color="green">103</FONT>        public RealVector solve(final RealLinearOperator a, final RealVector b)<a name="line.103"></a>
<FONT color="green">104</FONT>            throws NullArgumentException, NonSquareOperatorException,<a name="line.104"></a>
<FONT color="green">105</FONT>            DimensionMismatchException, MaxCountExceededException {<a name="line.105"></a>
<FONT color="green">106</FONT>            MathUtils.checkNotNull(a);<a name="line.106"></a>
<FONT color="green">107</FONT>            final RealVector x = new ArrayRealVector(a.getColumnDimension());<a name="line.107"></a>
<FONT color="green">108</FONT>            x.set(0.);<a name="line.108"></a>
<FONT color="green">109</FONT>            return solveInPlace(a, null, b, x);<a name="line.109"></a>
<FONT color="green">110</FONT>        }<a name="line.110"></a>
<FONT color="green">111</FONT>    <a name="line.111"></a>
<FONT color="green">112</FONT>        /** {@inheritDoc} */<a name="line.112"></a>
<FONT color="green">113</FONT>        @Override<a name="line.113"></a>
<FONT color="green">114</FONT>        public RealVector solve(final RealLinearOperator a, final RealVector b,<a name="line.114"></a>
<FONT color="green">115</FONT>                                final RealVector x0)<a name="line.115"></a>
<FONT color="green">116</FONT>            throws NullArgumentException, NonSquareOperatorException,<a name="line.116"></a>
<FONT color="green">117</FONT>            DimensionMismatchException, MaxCountExceededException {<a name="line.117"></a>
<FONT color="green">118</FONT>            MathUtils.checkNotNull(x0);<a name="line.118"></a>
<FONT color="green">119</FONT>            return solveInPlace(a, null, b, x0.copy());<a name="line.119"></a>
<FONT color="green">120</FONT>        }<a name="line.120"></a>
<FONT color="green">121</FONT>    <a name="line.121"></a>
<FONT color="green">122</FONT>        /**<a name="line.122"></a>
<FONT color="green">123</FONT>         * Performs all dimension checks on the parameters of<a name="line.123"></a>
<FONT color="green">124</FONT>         * {@link #solve(RealLinearOperator, RealLinearOperator, RealVector, RealVector) solve}<a name="line.124"></a>
<FONT color="green">125</FONT>         * and<a name="line.125"></a>
<FONT color="green">126</FONT>         * {@link #solveInPlace(RealLinearOperator, RealLinearOperator, RealVector, RealVector) solveInPlace},<a name="line.126"></a>
<FONT color="green">127</FONT>         * and throws an exception if one of the checks fails.<a name="line.127"></a>
<FONT color="green">128</FONT>         *<a name="line.128"></a>
<FONT color="green">129</FONT>         * @param a the linear operator A of the system<a name="line.129"></a>
<FONT color="green">130</FONT>         * @param m the preconditioner, M (can be {@code null})<a name="line.130"></a>
<FONT color="green">131</FONT>         * @param b the right-hand side vector<a name="line.131"></a>
<FONT color="green">132</FONT>         * @param x0 the initial guess of the solution<a name="line.132"></a>
<FONT color="green">133</FONT>         * @throws NullArgumentException if one of the parameters is {@code null}<a name="line.133"></a>
<FONT color="green">134</FONT>         * @throws NonSquareOperatorException if {@code a} or {@code m} is not<a name="line.134"></a>
<FONT color="green">135</FONT>         * square<a name="line.135"></a>
<FONT color="green">136</FONT>         * @throws DimensionMismatchException if {@code m}, {@code b} or<a name="line.136"></a>
<FONT color="green">137</FONT>         * {@code x0} have dimensions inconsistent with {@code a}<a name="line.137"></a>
<FONT color="green">138</FONT>         */<a name="line.138"></a>
<FONT color="green">139</FONT>        protected static void checkParameters(final RealLinearOperator a,<a name="line.139"></a>
<FONT color="green">140</FONT>            final RealLinearOperator m, final RealVector b, final RealVector x0)<a name="line.140"></a>
<FONT color="green">141</FONT>            throws NullArgumentException, NonSquareOperatorException,<a name="line.141"></a>
<FONT color="green">142</FONT>            DimensionMismatchException {<a name="line.142"></a>
<FONT color="green">143</FONT>            checkParameters(a, b, x0);<a name="line.143"></a>
<FONT color="green">144</FONT>            if (m != null) {<a name="line.144"></a>
<FONT color="green">145</FONT>                if (m.getColumnDimension() != m.getRowDimension()) {<a name="line.145"></a>
<FONT color="green">146</FONT>                    throw new NonSquareOperatorException(m.getColumnDimension(),<a name="line.146"></a>
<FONT color="green">147</FONT>                                                         m.getRowDimension());<a name="line.147"></a>
<FONT color="green">148</FONT>                }<a name="line.148"></a>
<FONT color="green">149</FONT>                if (m.getRowDimension() != a.getRowDimension()) {<a name="line.149"></a>
<FONT color="green">150</FONT>                    throw new DimensionMismatchException(m.getRowDimension(),<a name="line.150"></a>
<FONT color="green">151</FONT>                                                         a.getRowDimension());<a name="line.151"></a>
<FONT color="green">152</FONT>                }<a name="line.152"></a>
<FONT color="green">153</FONT>            }<a name="line.153"></a>
<FONT color="green">154</FONT>        }<a name="line.154"></a>
<FONT color="green">155</FONT>    <a name="line.155"></a>
<FONT color="green">156</FONT>        /**<a name="line.156"></a>
<FONT color="green">157</FONT>         * Returns an estimate of the solution to the linear system A &amp;middot; x =<a name="line.157"></a>
<FONT color="green">158</FONT>         * b.<a name="line.158"></a>
<FONT color="green">159</FONT>         *<a name="line.159"></a>
<FONT color="green">160</FONT>         * @param a the linear operator A of the system<a name="line.160"></a>
<FONT color="green">161</FONT>         * @param m the preconditioner, M (can be {@code null})<a name="line.161"></a>
<FONT color="green">162</FONT>         * @param b the right-hand side vector<a name="line.162"></a>
<FONT color="green">163</FONT>         * @return a new vector containing the solution<a name="line.163"></a>
<FONT color="green">164</FONT>         * @throws NullArgumentException if one of the parameters is {@code null}<a name="line.164"></a>
<FONT color="green">165</FONT>         * @throws NonSquareOperatorException if {@code a} or {@code m} is not<a name="line.165"></a>
<FONT color="green">166</FONT>         * square<a name="line.166"></a>
<FONT color="green">167</FONT>         * @throws DimensionMismatchException if {@code m} or {@code b} have<a name="line.167"></a>
<FONT color="green">168</FONT>         * dimensions inconsistent with {@code a}<a name="line.168"></a>
<FONT color="green">169</FONT>         * @throws MaxCountExceededException at exhaustion of the iteration count,<a name="line.169"></a>
<FONT color="green">170</FONT>         * unless a custom<a name="line.170"></a>
<FONT color="green">171</FONT>         * {@link org.apache.commons.math3.util.Incrementor.MaxCountExceededCallback callback}<a name="line.171"></a>
<FONT color="green">172</FONT>         * has been set at construction of the {@link IterationManager}<a name="line.172"></a>
<FONT color="green">173</FONT>         */<a name="line.173"></a>
<FONT color="green">174</FONT>        public RealVector solve(RealLinearOperator a, RealLinearOperator m,<a name="line.174"></a>
<FONT color="green">175</FONT>            RealVector b) throws NullArgumentException, NonSquareOperatorException,<a name="line.175"></a>
<FONT color="green">176</FONT>            DimensionMismatchException, MaxCountExceededException {<a name="line.176"></a>
<FONT color="green">177</FONT>            MathUtils.checkNotNull(a);<a name="line.177"></a>
<FONT color="green">178</FONT>            final RealVector x = new ArrayRealVector(a.getColumnDimension());<a name="line.178"></a>
<FONT color="green">179</FONT>            return solveInPlace(a, m, b, x);<a name="line.179"></a>
<FONT color="green">180</FONT>        }<a name="line.180"></a>
<FONT color="green">181</FONT>    <a name="line.181"></a>
<FONT color="green">182</FONT>        /**<a name="line.182"></a>
<FONT color="green">183</FONT>         * Returns an estimate of the solution to the linear system A &amp;middot; x =<a name="line.183"></a>
<FONT color="green">184</FONT>         * b. The solution is computed in-place (initial guess is modified).<a name="line.184"></a>
<FONT color="green">185</FONT>         *<a name="line.185"></a>
<FONT color="green">186</FONT>         * @param a the linear operator A of the system<a name="line.186"></a>
<FONT color="green">187</FONT>         * @param m the preconditioner, M (can be {@code null})<a name="line.187"></a>
<FONT color="green">188</FONT>         * @param b the right-hand side vector<a name="line.188"></a>
<FONT color="green">189</FONT>         * @param x0 the initial guess of the solution<a name="line.189"></a>
<FONT color="green">190</FONT>         * @return a reference to {@code x0} (shallow copy) updated with the<a name="line.190"></a>
<FONT color="green">191</FONT>         * solution<a name="line.191"></a>
<FONT color="green">192</FONT>         * @throws NullArgumentException if one of the parameters is {@code null}<a name="line.192"></a>
<FONT color="green">193</FONT>         * @throws NonSquareOperatorException if {@code a} or {@code m} is not<a name="line.193"></a>
<FONT color="green">194</FONT>         * square<a name="line.194"></a>
<FONT color="green">195</FONT>         * @throws DimensionMismatchException if {@code m}, {@code b} or<a name="line.195"></a>
<FONT color="green">196</FONT>         * {@code x0} have dimensions inconsistent with {@code a}<a name="line.196"></a>
<FONT color="green">197</FONT>         * @throws MaxCountExceededException at exhaustion of the iteration count,<a name="line.197"></a>
<FONT color="green">198</FONT>         * unless a custom<a name="line.198"></a>
<FONT color="green">199</FONT>         * {@link org.apache.commons.math3.util.Incrementor.MaxCountExceededCallback callback}<a name="line.199"></a>
<FONT color="green">200</FONT>         * has been set at construction of the {@link IterationManager}<a name="line.200"></a>
<FONT color="green">201</FONT>         */<a name="line.201"></a>
<FONT color="green">202</FONT>        public abstract RealVector solveInPlace(RealLinearOperator a,<a name="line.202"></a>
<FONT color="green">203</FONT>            RealLinearOperator m, RealVector b, RealVector x0) throws<a name="line.203"></a>
<FONT color="green">204</FONT>            NullArgumentException, NonSquareOperatorException,<a name="line.204"></a>
<FONT color="green">205</FONT>            DimensionMismatchException, MaxCountExceededException;<a name="line.205"></a>
<FONT color="green">206</FONT>    <a name="line.206"></a>
<FONT color="green">207</FONT>        /** {@inheritDoc} */<a name="line.207"></a>
<FONT color="green">208</FONT>        @Override<a name="line.208"></a>
<FONT color="green">209</FONT>        public RealVector solveInPlace(final RealLinearOperator a,<a name="line.209"></a>
<FONT color="green">210</FONT>            final RealVector b, final RealVector x0) throws<a name="line.210"></a>
<FONT color="green">211</FONT>            NullArgumentException, NonSquareOperatorException,<a name="line.211"></a>
<FONT color="green">212</FONT>            DimensionMismatchException, MaxCountExceededException {<a name="line.212"></a>
<FONT color="green">213</FONT>            return solveInPlace(a, null, b, x0);<a name="line.213"></a>
<FONT color="green">214</FONT>        }<a name="line.214"></a>
<FONT color="green">215</FONT>    }<a name="line.215"></a>




























































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